Definition of the Magnetic Field With a brief history of electromagnetism, and a general understanding of what conditions give rise to a magnetic field, we may now precisely define the magnetic field. Magnetic Force when Moving Charges are not Perpendicular We disucussed the special case in which the moving charge moves perpendicular to the magnetic field. This perfectly perpendicular situation is uncommon. In more normal circumstances the magnetic force is proportional to the component of the velocity that acts in the perpendicular direction. If a charge moves with a velocity at an angle θ to the magnetic field, the force on that particle is defined as: F = If you are familiar with vector calculus, you will notice that this can be simplified in terms of cross products: forceequation* = This last equation is the most complete; the cross product of two vectors is always perpendicular

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Unformatted text preview: to both vectors, providing the correct direction for the direction of our force. Having established this equation, let us take a moment to analyze its implications. First, it is clear that a charge moving parallel to the magnetic field experiences no force, as the cross product is zero. Second, the magnitude of the force on the charge varies directly not only with the magnitude of the charge, but of the velocity as well. The faster a charged particle travels, the more force it will feel in the presence of a given magnetic field. This equation forms a basis for our study of electromagnetism. From it we will be able to derive the fields created by various wires and magnets, and derive some properties of the magnetic field....
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